A Dissipation-Free, Sharp Interface Method for High-Fidelity Compressible Multiphase Flow Simulations

We introduce a novel, quasi-dissipation-free method for simulating compressible multiphase flows. The governing equations are based on the six-equation model with mechanical relaxation. A dissipation-free semi-discrete formulation is used in the bulk phases, integrated with fourth-order Runge-Kutta time stepping. At sharp interfaces, the scheme is hybridized—both spatially and temporally—with a semi-Lagrangian geometric Volume-of-Fluid (VOF-PLIC) method that transports discontinuous phasic quantities with second-order accuracy. This hybrid approach preserves dissipation-free properties throughout, including across interfaces. Dissipation is introduced only where necessary to stabilize regions with significant temporal error, without compromising overall accuracy. By minimizing numerical dissipation, the solver exposes the need for subgrid-scale models to handle under-resolved turbulence, shocks, and breakup—making it an ideal platform for their development and application. Simulations of a shock impacting a liquid droplet at high Reynolds and Weber numbers demonstrate the method's accuracy and robustness in complex multiphase environments relevant to hypersonic flows.